Sixteen players `P_(1),P_(2),P_(3)….., P_(16)` play in tournament. If they grouped into eight pair then the probability that `P_(4)` and `P_(9)` are in different groups, is equal to

P_(1),P_(2),P_(3),are:

Sixteen players S_(1) , S_(2) , S_(3) ,…, S_(16) play in a tournament. Number of ways in which they can be grouped into eight pairs so that S_(1) and S_(2) are in different groups, is equal to

Sixteen players S_(1),S_(2),...,S_(16) play in a tournament.They are divided into eight pairs at random.From each pair a winner is decided on the basis of a game played between the two players of the pair.Assume that all the players are of equal strength.Find the probability that the player S_(1) is among the eight winners.

8n players P_(1),P_(2),P_(3)……..P_(8n) play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in 3 where the players are paired at random in each round. If it is given that P_(1) wins in the third round. Find the probability that P_(2) looses in the second round.

16 players P_(1),P_(2),P_(3),….P_(16) take part in a tennis tournament. Lower suffix player is better than any higher suffix player. These players are to be divided into 4 groups each comprising of 4 players and the best from each group is selected to semifinals. Q. Number of ways in which they can be divided into 4 equal groups if the players P_(1),P_(2),P_(3) and P_(4) are in different groups, is:

16 players P_(1),P_(2),P_(3),….P_(16) take part in a tennis tournament. Lower suffix player is better than any higher suffix player. These players are to be divided into 4 groups each comprising of 4 players and the best from each group is selected to semifinals. Q. Number of ways in which these 16 players can be divided into four equal groups, such that when the best player is selected from each group P_(6) in one among them is (k)(12!)/((4!)^(3)) the value of k is

Eight players P_(1),P_(2),P_(3),............P_(8), play a knock out tourrament.It is known that whenever the players P_(i) and P_(j), play,the player P_(i) will win if i